Find the value of $\sin\frac{5\pi}{36}\cos\frac{\pi}{36}+\sin\frac{\pi}{36}\cos\frac{5\pi}{36}$sin5π36cosπ36+sinπ36cos5π36 in exact form.

Find the exact value of $\cos\frac{21\pi}{10}\cos\frac{\pi}{10}+\sin\frac{21\pi}{10}\sin\frac{\pi}{10}$cos21π10cosπ10+sin21π10sinπ10.

Find the exact value of $\frac{\tan\frac{2\pi}{9}-\tan\frac{\pi}{18}}{1+\tan\frac{2\pi}{9}\tan\frac{\pi}{18}}$tan2π9−tanπ181+tan2π9tanπ18.

Suppose $\cos A=\frac{3}{5}$cosA=35 and $\sin B=\frac{15}{17}$sinB=1517, where $00<A<π2 and $00<B<π2.

Manipulate trigonometric expressions

Apply trigonometric methods in solving problems